I'm sure you all have heard the saying "Starve a fever, but feed a cold." It goes through my head every time I take my daughter's temperature.
Well, I researched it and it is SO not true and public health officials have been working for years to debunk the age old maxim.
According to Straight Dope the saying dates all the way back to 1574. At least the "starve a fever part", no one is sure when the second half was added.
There seems to be no scientific evidence that supports fasting as a cure for a fever. When running a fever, it is best not to stress the body by not eating. Chances are high (sorry for the pun) rich foods will have no real appeal if you're feverish. Stick to simple broths and toast.
If you have a cold there is nothing wrong with eating, but you just might not be able to taste it.